On Engineering the Appearance of Cyberspace

F. Kenton Musgrave
Pandromeda, Inc.
musgrave@pandromeda.com

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts...A graphic representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellation of data. Like city lights, receding..."

--William Gibson, "Neuromancer"

Introduction

Gibson's definition of cyberspace in a science fiction novel in 1984 was remarkably prescient. Today's world wide web is the beginning of the organization of and access to the data Gibson refers to, but as a visualization it is embryonic and, so far, unremarkable--it is simply hypertext, not the immersive environment envisioned by Gibson. The fact that we are constrained to such tame presentation is primarily attributable to the twin problems of rapid transfer of large amounts of data and computing high quality renderings in real time. When we achieve near-instant access to the requisite data and the capacity to generate detailed immersive, interactive visuals on the fly, cyberspace will reach is vaunted potential as a useful, immersive virtual reality.

But what should it look like once we've engineered the capacity to create it? Gibson's vision is rather limited here. Lines of light and glowing blue pyramids provide nice imagery for a science fiction novel, but what we require is a highly functional and truly powerful design for the user interface that is cyberspace. It is well established that the main conduit of information from the senses to the human brain is through vision. Thus we are going to need a carefully engineered and well-justified visual manifestation of cyberspace to fully tap its potential to organize and convey the information it embodies.

Navigation of the representation is a key issue. Early experience with virtual reality indicates that navigation of synthetic 3D spaces is difficult for humans. Keeping track of one's orientation and relative and absolute positions in the synthetic environment are notoriously difficult, perhaps because of the alien appearance of the environment, its simplicity (read: lack of visual cues) compared to reality, and/or the limited engagement of our senses in current VR technology. Or perhaps it is because we, as biological entities, are better designed to deal with the kind of environment in which we evolved than with abstract, synthetic spaces.

Claims

We have a biological heritage: primates roaming forests and the savanna. Invoking the neural net model, our "wetware" may be inherently optimized for certain image recognition tasks. Primary among these is apprehending nonverbal communication of other individuals of our species: we feature exquisite sensitivity to the nuances of people's facial appearances and the dynamics thereof. External to our troop of primates, we are engineered by evolution to deal effectively with features of our natural environment: terrain and other natural phenomena.

So what is the best visual manifestation for cyberspace? It should be familiar, and suited to the hardwired specializations of our neural net. That is, it should appear like Nature as our ancestors over the eons knew it, which was far more intimately than modern humans.

What are the fundamental features of this "natural" cyberspace? Of course, there are the standard features of a landscape scene: terrain, clouds, atmospheric effects, water, etc. Realism in these has been and will continue to be addressed to ever greater satisfaction in the literature of computer graphics research. Those are the obvious phenomena. I wish to point some more subtle, yet equally essential, requisite features of a "natural" cyberspace: 1) It should be locally two-dimensional, like the surface of the Earth. 2) On intermediate scales it should be spherical, like a planet. 3) On the largest scale it should be three dimensional, like the universe we inhabit. 4) The geometry used for its representation should be, for the most part, fractal.

Let me now motivate and justify these claims.

The locally planar appearance of our planet is compelling enough that the "flat earth" model held sway as a sufficient model of Earth quite recently in our cultural history. Furthermore, we primates generally enjoy mobility only in two-and-one-half dimensional space, that is, on the surface of the earth, with occasional forays into trees and such. Also, which way is "up" is rarely in doubt. These factors greatly simplify our navigational challenges. Experience with the Bryce synthetic landscape generation software product indicates that naive users find Bryce much easier to learn and operate than general 3D graphics applications. We conjecture that this may be because A) the user is generally dealing with a 2 1/2D space rather than full 3D, and B) the default natural environment features a horizon and gradated-by-altitude sky which make it obvious which way is "up." Given this familiar and non-threatening initial environment a new user, one with no prior experience in 3D graphics, naturally makes straightforward progress in learning the more recondite aspects of general 3D graphics without even being aware of how difficult mastering them can be. Simply stated, 2 1/2D environments appear to be natural and intuitive for the average person.

The global context for landscapes is a planet: a sphere, a globe. This alone could justify the claim that "natural" cyberspace should be spherical at intermediate scales. But there is another advantage indicating this geometry: it is topologically convenient. A spherical surface is finite but unbounded. This means that we can have our locally planar geometry, without worrying about falling off the edge of our necessarily finite world. It can also be a convenient boundary condition assumption for simulations such as artificial ecosystems. Finally it can obviate, through spatial disconnection, the problem of engineering transitions between disparate models. Thus, for instance, no one would need to labor over making a seamless transition between the stylized appearance of an environment designed for interactive shoot-'em-up gameplay and that of an environment designed to host a set of non-real time, scientifically accurate simulations of natural processes.

Planets, in turn, reside in the familiar context of three-dimensional space. Using three dimensions yields the maximum usable space by employing the highest usable dimension--human intuition being ill equipped to deal with higher-dimensional spaces. Three-dimensional space is the obviously the way to organize our layout on largest scale not only because it maximizes the total usable space, but also because it can vastly increase the local density of information (this being only occasionally a virtue). Maintaining the argument that Nature's appearance will always be the most comfortable, familiar and efficacious of our visual options, the obvious way to lay out our universe of planets is to imitate the universe as we know it: planets reside in solar systems, solar systems in galaxies, galaxies in clusters, and clusters in superclusters. The real universe is inhomogeneous on large scales: there are vast voids between concentrations of galaxies. This, fortunately, can correspond to the good practice in visual design of judicious use of empty space (so-called "negative space") to reduce clutter and guide the viewer's attention. That is, the sheets-and-voids distribution that characterizes the largest scale structure of matter in the visible universe just might lend itself naturally to good visual design and effective imposition of (more or less arbitrary) order on the vast quantities of data that cyberspace is designed to represent for human consumption.

The Fractal Geometry of Cyberspace

One must choose a geometry to use in constructing the visual representation of cyberspace. We have two realistic choices: Euclidean or fractal. The passage where Gibson defined "cyberspace" evokes a primarily Euclidean visualization: "lines of light...like city lights, receding..." Auspiciously, he also mentions "clusters and constellation of data," evoking the fractal geometry that generally better characterizes the forms found in Nature. We're all familiar with the shapes of Euclidean geometry: lines, planes, spheres, cubes, cones, etc. Euclidean geometry is excellent for describing things made by humans, and generally poor for describing the complexity of form in Nature. The opposite is true of fractal geometry. One might conclude that, since cyberspace and everything in it is a human-made artifact, Euclidean geometry is the obvious choice for its visual representation. This is probably so, for the artifacts representing the information content in cyberspace. That is, there will be cities and schematics of devices and text and such on the planets that comprise cyberspace; these should be represented in the familiar, Euclidean way. What is better made fractal is the visual context for that content. I maintain that the context should be like Nature, and Nature is largely fractal. Yet it's not that simple and clear-cut, either.

I assume that the reader is familiar with Euclidean geometry; let me now give a brief overview of fractal geometry. Random fractals or so-called "scaling noises" such as fractional Brownian motion [4] characterize many structures in Nature. Deterministic fractals such as the famous Mandelbrot set, or M-set, and the von Koch snowflake constitute another class of fractals. (Interestingly, certain deterministic fractals such as the von Koch snowflake and the Peano curve [3] are even locally Euclidean, e.g., are comprised of straight line segments.) Fractal geometry can be most succinctly characterized as dilation symmetry, or invariance (perhaps only statistical) over changes in scale. That is, zooming in and zooming out, one sees pretty much the same thing at different scales; appearance remains similar, hence the term self-similarity is used to characterize fractals. Fractal objects appear complex, due to the amount of detail evoked by this repetition of form over a range of scales. This apparent complexity may be deceivingly simple, however, as both the basic form and the rules of repetition may be very simple. How, then, do fractals mix with generally simpler Euclidean forms in our synthetic universe?

We primates are social beasts, and there will inevitably arise cyberManhattans: "hot properties," local spots where "everyone will want to be" in the vast cyberuniverse. Again, to maintain the analogy with real cities, we will probably construct them using Euclidean geometry. Yet despite its complexity and the fact that it is not generally a good language for human-made form, fractal geometry has application in constructing cyber-cities: as in real cities, space in cyber-cities will be at a premium. Just because your company grew from two employees to owning Microsoft doesn't mean you can necessarily expand your corporate headquarters in cyberSeattle to occupy half of downtown--that space will already be occupied. But scale is an entirely arbitrary concept in cyberspace; there is no standard meter, no inherent size to anything. Thus it won't matter how "large" you loom in cyberspace, but rather how much information you have, that people want to access. Using a fractal representation, you can grow "inward" by adding ever more detail that can be seen by zooming farther and farther in to your cyberconstruct. Growing inward like this will obviate the need to occupy ever more space, to expand one's hegemony by conquest or cyberimperialism. The ability to grow inward may spawn a new esthetic based, in the fine artistic tradition of rejecting contemporary values, on the idea that smaller is better, that getting the most content into the smallest space is a greater accomplishment than growing to be as large as possible. The ability to grow inward, fractally, obviates the problem of available space in our cyber-cities.

Two other issues indicate the use of fractal geometry in the construction of cyberspace: first the transfer, and second the realistic rendering, of highly complex scenes. The problem of aliasing is too recondite to address here, but let us say that one of the main problems in rendering very complex scenes arises from the difficulties in cramming more information in the pixel grid, or raster,that comprises the image, than that grid can accurately represent. The problem is inevitable, because of the complexity of cyberspace. Aliasing shows up as highly unnatural and objectionable artifacts in still images, and worse artifacts still in moving images. Fortunately, due to their constructive or "procedural" nature [1], fractals can be adaptively band-limited for alias-free rendering. That is, their construction can limit their detail to that which the raster can accurately represent. Furthermore, their procedural character ensures that everyone can explore the same synthetic universe of unlimited visual richness, without the need for hypernet bandwidth or huge, mirrored database servers simply to dish up the visual representation--as opposed to the information content--of that universe. This is because the visual richness of fractal models is an emergent property of their computation. A very simple model and a few parameter settings are sufficient to generate an entire world, with potentially unlimited detail. [2] A beauty of the fractal representation is that the model is tiny, in comparison to the visual result. The model consists only of the basic shape and the rules for its repetition; all details emerge from the computation. This solves the bandwidth problem inherent in transferring from remote repositories to users, complex representations of cyberspace--the place, as opposed to the content or information accessed there--leaving the network bandwidth free for transferring that content, which is what we'll go into cyberspace for, in the first place.

Conclusions

In conclusion, I'd like to reiterate that the natural, fractal universe I am advocating is not an end in itself, but rather a context for the information content that cyberspace is designed to make accessible to humans. Cyberspace is strictly for human consumption. The machines do not need it; they do very well with their streams of binary code. Cyberspace is a visualization tool designed to make the exponentially growing stores of information entrusted to the computers, and its inherent value, available to humans who generally do poorly at comprehending binary-encoded information.

The "natural" cyberspace I am proposing is an efficacious setting for entertainment, like games and Myst-style puzzles, for synthetic ecosystems, simulated cities and civilizations, artistic creations, meditative spaces, and raw data retrieval. The suggested hierarchy going from 3D to 2 1/2D to 2D preserves advantages of the evolved human faculties for interaction with our environment. Extensive use of fractals imparts visual richness, compact representation, and a natural visual character also suited to our naturally evolved faculties. It is familiar and expandable. It is as politically and aesthetically neutral and non-controversial as such an important and soon-to-be ubiquitous aspect of human life can be made. Most importantly, is has the potential to be made as beautiful as the universe we inhabit.

References

[1] Ebert, D.S., ed. Textures and Modeling: A Procedural Approach. 2nd ed. 1998, Academic Press:Cambridge, MA.

[2] Gibbs, W.W., Playing Slartibartfast with Fractals, in Scientific American1996, p. 36-37.

[3] Mandelbrot, B.B., The Fractal Geometry of Nature. 1982, NewYork: W. H. Freeman and Co.

[4] Peitgen, H.O. and D. Saupe, ed. The Science of Fractal Images.1988, Springer-Verlag: New York.